I don't like the NIV, but nothing to do with leaving verses out. It tends to degrade the deity of Christ. That being said, I was raised on KJV, have a huge stock of memory verses in it, but I don't read it because I have never learned 16th century English. Words change and English is no exception.
Case in point - Matt 6:6
"But thou, when thou prayest, enter into thy closet." KJV
Ok, I confess I like having 2nd person singular. But I also don't really know how to use it, although I can figure it out reading it. But CLOSET. In King James time, a closet was a room where people met to discuss things and be together.
Fast forward to the 21st century, and literalists are kneeling under their clothes hangers!
Even King James 2000 Bible says:
"But when you pray, enter into your room,"
That really doesn't catch the meaning of the original Greek.
ταυμείν - a storeroom, innermost secret room. This was a place where the disciples gathered together to pray. Not about individual prayer, and I don't see a translation that reflects this. You might well imagine why they were praying in secret, especially towards the end of Jesus ministry!
Regarding the missing verses, there are many early manuscripts today of the Bible. In King James day, not so much. He basically translated from the Vulgate, and Erasmus. Now Erasmus spoke excellent Greek and Hebrew, and even in his day, he found lots of manuscripts that deviated from Jerome's version of the Bible. Who did not speak the languages very well. But Erasmus wanted the new Bible to reflect some of the errors he found in translation - Catholic Church vetoed it, and so King James contains some errors that come from Jerome!
A further issue is that most of the manuscripts we have today come from the Byzantine tradition. Greeks like to make little comments in the margins, and those were eventually added as text to the Bible. Other traditions, were much stricter about comments, and that is why the earliest manuscripts do not have many verses. (I agree, put it in brackets or italics - let the reader chose!)
If you really want to find out about variations, my advice is to pick up a copy of the United Bible Societies Greek New Testament. It has literally every variation known, most of which are just copyist errors.
Of course, then you have to learn Greek. It was one of the best things I ever did!
I do read about 10 versions, comparing to the Greek and Hebrew, but for personal devotions I stick to an ESV Study Bible. It does put down a few variations, and admits when things are not in the earliest manuscripts. It is a bit wooden, but seems to stick to the original languages a lot closer than most other translations, esp. word order and not smoothing it out too much.